{"paper":{"title":"Sharp large time behaviour in N -dimensional Fisher-KPP equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jean-Michel Roquejoffre (IMT), Luca Rossi (CNRS), Violaine Roussier-Michon (IMT)","submitted_at":"2019-03-27T07:29:19Z","abstract_excerpt":"We study the large time behaviour of the Fisher-KPP equation $\\partial$ t u = $\\Delta$u + u -- u 2 in spatial dimension N , when the initial datum is compactly supported. We prove the existence of a Lipschitz function s of the unit sphere, such that u(t, x) converges, as t goes to infinity, to U c * |x| -- c * t + N + 2 c * lnt + s $\\infty$ x |x| , where U c * is the 1D travelling front with minimal speed c * = 2. This extends an earlier result of G{\\\"a}rtner."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.11274","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}